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Solve ANY GED Math Inequality!

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in this video we're going to go over how

to do inequalities on the ged

and they could give you word problems

like this

algebraic ones like this

or number line ones like this

so we'll go over all of them

now the first one your wedding food

budget is 14.50

but let's pause there

look at the end we notice we have 14.50

we're either gonna stay above or below

that amount here

so let's break down these symbols

when it goes in this direction that

means more than or greater than

and then this one less than

and you could remember it because you

could turn the top one into a g the

bottom one and now

okay but this statement saying we're

going to spend this looks like an l less

than 1450

and that's what we want because we want

to stay under our budget so that one is good

good

the next one would say we're going to

spend greater than 1450 but that's no good

good

so as you could see a and c those might

be it b and d they're out

the next thing we want to find is what

are we going to do with x

that's the number of people

are we going to multiply it by 28 or by 500

500 but

but

the meals are 28 per person

we have x number of people

so we want to multiply 28 times x

so it's gonna have to be that first one a

because the caterer we just pay that one time

time

so we just add that into the mix there

okay not too bad but let's check out

another one

now let's jump to the end here because

we want to earn more than 500 this week

so let's look at these symbols

well the first one this looks like an l

less than 500 no good

but this one greater than more than 500

that's great let's keep that and same

thing on the bottom

okay get rid of a and c

now the question is what are we going to

multiply 30 by

well we could either do it by this or this

this

but 30 represents the number of hours

we earn 12 dollars per hour

so therefore those are the two we want

to multiply

because b would say okay we work 30

hours but we only make 12 cents per hour

but that's no good so it's got to be d

that last one there

and then finally our sales is x

and we're going to get 12 of that amount

so that's why we multiply it by point 12.

12.

same thing as 12

okay one other one

now in this case the answers are all

just one number

when that happens they've actually

solved the inequality so let's go ahead

and grab that

now if you've solved equations before

it's the exact same process but if not

no worries

the goal is to get x all by itself

but to do that we don't want that

fourteen thousand five hundred

so the first thing we're going to do is

subtract that

whatever you do to one side of the

problem it gets split right there you're

going to go ahead and do it to the right

side as well

and then that'll cancel these guys

drop down the negative 32x

then 100 minus 14 500 that'll give us that

that

whatever is in front of x is being

multiplied by x

we want to do the opposite

opposite of multiplication

divide by negative 32

and we'll do it to both sides there

okay those will cancel

and then

whatever this turns into this division

is going to give us the answer

however there's one other important aspect

aspect

when you divide by a negative with inequalities

inequalities

it's going to flip this

because this is a greater than it's

going to go ahead and flip it to a less than

than

but let's go ahead and do this with the

calculator let's do negative 14 400

divided by negative 32 450

450

so therefore x less than or equal to 450.

450.

now x in this case represents miles

we're driving on a full tank of gas

we're seeing how far we could go

so the number of miles is going to be

less than or equal to 450

okay let's just look at the algebraic

ones now

same idea as what we were just doing on

the previous problem let's check it

now when you solve an equation it just

has an equal sign when you solve an

inequality it's got a greater than or

less than

but it's still the same method for both

of these

okay so same thing we want to get x by

itself but we have a minus six

let's get rid of it let's add six

and then same thing on the other side

let's do it

these will cancel but let's break out

the calculator

because now we've got four thirds

you could use that fraction button right

there n over d

and then plus six

okay 22 over 3.

so that's on the right side and then

this one just drops straight down

but once again when you have something

in front of x that's multiplied by x

we want to get rid of it so we want to

do the opposite we're going to divide

both sides by two-thirds

that'll get rid of these

and then let's do it with the calculator here

here

we'll start off with 22 over three this

calculator is amazing same one you use

on the ged

but then divided by another fraction two

over three

ba boom eleven

eleven

kinda surprising but the fractions cancel

cancel

it's a positive so we don't flip the

sign we just keep it a greater than and

that's it

so final answer x is greater than or

equal to 11.

okay let's do one last version of this

with parentheses

because in this case you always want to

start with distribution

in other words you're going to go ahead

and multiply that thing in front times 8

so let's do that

okay our fraction we could go ahead and

do negative three

down two

negative twelve

so let's bring down the left the less

than or equal to negative 12 and then

just tack on the y right there

now we're going to multiply negative

three halves times twenty let's do it we

could start off with the negative this

time three down two

times 20

negative 30 so we'll put it as a minus

30 there

but once again we want to get y by

itself we want to get rid of that minus

30. we'll do the opposite we'll add 30

to both sides

that'll get rid of them there

the left side that turns into 42

and then negative 12y right there

but you know what to do they're next to

each other so as you've seen the last

step is always division

divide both sides by negative 12.

those will cancel

but don't forget

you just divided by a negative so we're

gonna have to flip the sign

okay 42 divided by negative 12 that'll

get us negative 3.5

goes from a less than or equal to to a

greater than or equal to

and we're home free

unfortunately it's not the same as one

of these just yet

so imagine that this is a little pac-man

and this is its mouth

so it's eating negative 3.5 it always

eats the bigger number

which of these is doing the same thing

well that first one that pac-man is also

eating negative 3.5

so it's the same thing as a there

now students often wonder and ask why

does dividing by a negative flip the sign

sign

let's look at an example real quick

okay 4 is greater than 2

no surprise

but let's divide both sides by a negative

negative

4 divided by negative two negative two

two divided by negative two negative one

however when you look at a number line

whatever is further to the right is bigger

bigger

so surprisingly negative one is bigger

than negative two

in other words we went from a greater than

than

to a less than

and that's why it flips because when you

go into the negatives then it's backwards

backwards

whatever is actually a smaller negative

is technically bigger

and one last type here

okay which represents this

okay x is greater than or equal to

negative 1.5

one thing you could look at is this

equal sign

means that the hole is going to be

filled in

so could be c could be d let's get rid

of a and b

and then we know we say it is greater

than so it's going to be to the right

so it's going to have to be c

one of the ways my students remember it

is this looks like an arrow pointing to

the right

so you want the arrow also to point to

the right

and then the other ones if you're

curious or these ones

just keep in mind when it's greater than

it's going to be to the right

and what's nice is less than is to the

left so l and l

okay these are the main types of

inequalities that show up on the ged

let me know what questions and issues

you run into you got these we'll see in

the next video toodles

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